Sato-Tate Conjecture for Bianchi Modular Forms

Explore potential automorphy results implying the Ramanujan and Sato-Tate conjectures for regular algebraic cuspidal automorphic representations of GL(2) over an imaginary quadratic field in this 1-hour 9-minute lecture. Delve into the generalization of results from the "10 author paper," which previously focused on cohomological weight 0, as presented by James Newton from the University of Oxford. Examine new components of this joint work with George Boxer, Frank Calegari, Toby Gee, and Jack Thorne, including applications of Newton's work with Ana Caraiani on local-global compatibility, aspects of Dwork hypersurfaces' cohomology investigated by Lie Qian, and a generic reducedness result for mod p fibres of local deformation rings. Gain insights into advanced topics in number theory and automorphic forms as presented at the Institut des Hautes Etudes Scientifiques (IHES).